An improved bald eagle search algorithm fused with multiple strategies(IBES) is proposed to address the shortcomings of the bald eagle search algorithm(BES), such as the global search performance is not coordinated with the local exploitation capability and it is easy to fall into local optimum. The use of convex adaptive control factors enables the algorithm to dynamically adjust the position update equations to modify the model according to the search process during the iterative optimization, thus achieving adaptive optimization and effectively balancing the global search performance and local exploitation capability of the algorithm. The refracted opposition-based learning mechanism is used to discover the corresponding solution by refracting the current solution of the problem in its solution space, which increases the probability of finding the optimal solution and improves the solution accuracy and convergence speed of the algorithm. At the same time, the directional recombination and induced mutation strategy is used to achieve the recombination and mutation of the multi-dimensional information of population individuals, improve the individual quality and population diversity, increase the probability of the algorithm escaping from local optimum, and raise the searching precision. The optimal value, mean value, standard deviation and average convergence algebra are used as evaluation indexes of the algorithm performance, and numerical simulation experiments are conducted for 10 different benchmark test functions. The experimental results verify the effectiveness of the proposed improved method and the superiority of the IBES. In addition, the PID neural network controller optimized by the IBES has a fast response, small overshoot, and short regulation time, which further verifies the practicality of the algorithm.